Antiferromagnetism and Phase Transitions in Non-Centrosymmetric
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Antiferromagnetism and phase transitions in non-centrosymmetric UIrSi3 J. Valenta1, F. Honda2, M. Vališka1, P. Opletal1, J. Kaštil3, M. Míšek3, M. Diviš1, L. Sandratskii4, J. Prchal1, and V. Sechovský1 1Charles University, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Ke Karlovu 5, Prague 2, Czech Republic 2Tohoku University, Institute for Materials Research, Narita-cho 2145-2, Oarai, Ibaraki, Japan 3Institute of Physics AS CR, Na Slovance 1999/2, Prague 8, Czech Republic 4Max-Planck-Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany Abstract Magnetization and specific heat measurements on a UIrSi3 single crystal reveal Ising-like antiferromagnetism below TN = 41.7 K with easy magnetization direction along the c-axis of tetragonal structure. The antiferromagentic ordering is suppressed by magnetic fields > Hc (µ0Hc = 7.3 T at 2 K) applied along the c-axis. The first-order metamagnetic transition at Hc exhibits asymmetric hysteresis reflecting a slow reentry of the complex ground-state antiferromagnetic structure with decreasing field. The hysteresis narrows with increasing temperature and vanishes at 28 K. A second-order metamagnetic transition is observed at higher temperatures. The point of change of the order of transition in the established H-T magnetic phase diagram is considered as the tricritical point (at Ttc = 28 K and µ0Htc = 5.8 T). The modified-Curie-Weiss-law fits of temperature dependence of the a- and c-axis a c susceptibility provide opposite signs of Weiss temperatures, p ~ -51 K and p ~ +38 K, respectively. This result and the small value of µ0Hc contrasting to the high TN indicate competing ferromagnetic and antiferromagnetic interactions responsible for the complex antiferromagnetic ground state. The simultaneous electronic-structure calculations focused on the total energy of ferromagentic and various antiferromagnetic states, the U magnetic moment and magnetocrystalline anisotropy provide results consistent with experimental findings and the suggested physical picture of the system. 1 Introduction The growing interest in materials adopting crystal structures which have no center of 1 symmetry was boosted by the discovery of unconventional superconductivity in CePt3Si . The absence of a center of inversion in the crystal structure along with a Rashba-type antisymmetric spin-orbit (s-o) coupling2, 3 leads to the possibility of a superconducting state with an admixture of spin-triplet and spin-singlet pairs4. The Rashba s-o coupling in materials crystallizing in a noncentrosymmetric crystal structure also causes spin-splitting of the Fermi surface into two Fermi surfaces, which has many intriguing implications in various branches of physics including magnetism5. The BaNiSn3-type structure (I4mm) illustrated in Fig. 1 is one of the ternary variants of the BaAl4 tetragonal structure. It is adopted by several RTX3 compounds (R: rare earth, T: transition metal, X: p-electron element). The R atoms occupy the corners and the body center of the tetragonal structure whereas the T-X sublattice is non-centrosymmetric. The lack of an inversion center in the crystal structure brings about a nonuniform lattice potential V(r) along the c-axis, whereas the nonuniform lattice potential within the a-b plane is canceled out6. The RTX3 compounds with Ce are of high research interest because they exhibit diverse interesting phenomena like superconductivity with a high critical field, pressure induced superconductivity near a quantum critical point, coexistence of antiferromagnetism and superconductivity, vibron states, etc.7-12. The magnetic ordering in these materials is usually antiferromagnetic (AF) with complex propagation vectors13-16 which indicate competing ferromagnetic and antiferromagnetic exchange interactions. FIG. 1. Crystal structure of UIrSi3. Contrary to rare-earth compounds where the magnetic moment is usually born in the localized 4f-electrons, the 5f-electron wave functions in U intermetallics lose, to a considerable extent, their atomic character due to the mutual overlap between neighboring U ions and due to the hybridization of 5f-states with valence electron states of ligands (5f-ligand hybridization). The large direct overlap of 5f-wave functions by rule prevents formation of a rigid atomic 5f- electron magnetic moment in materials in which the distance of nearest-neighbor U atoms is smaller than the Hill limit (340-360 pm)17. On the other hand, the layout of U-U nearest neighbors carrying 5f-electron orbital moments in the crystal lattice usually determines the 2 huge magnetocrystalline anisotropy with the easy magnetization axis perpendicular to the strong U-U bonding planes or chains18. The 5f-ligand hybridization has similar but more subtle effects on U magnetism. Its role strengthens in compounds with a lower U content in which the U ion surrounding ligands prevent the direct U-U bonds19, 20. As concerns the magnetic coupling the direct overlap of 5f-wave functions of U neighbors is responsible for the direct exchange interaction between U nearest-neighbor magnetic moments whereas the 5f-ligand hybridization mediates the indirect exchange interaction between moments of U ions neighboring the involved ligand. Only two uranium compounds adopting the tetragonal BaNiSn3-type structure are known, namely, UIrSi3 and UNiGa3. Both have been studied in the form of polycrystals only and 21 22 reported to order antiferromagnetically below 42 K (UIrSi3) and 39 K (UNiGa3) , respectively. This paper is dedicated to the result of our effort to advance understanding of the physics of one of these two compounds. We have prepared a UIrSi3 single crystal, characterized its composition and crystal structure and measured the magnetization and specific heat in a wide range of temperatures and external magnetic fields. The results confirm that UIrSi3 becomes antiferromagnetic below the Néel temperature TN = 41.7 K with strongly anisotropic response to an external magnetic field. In the magnetic field along the c-axis it undergoes a metamagnetic transition (MT) at a critical field Hc (µ0Hc = 7.3 T at 2 K) into a field-polarized state with a magnetic moment of ~ 0.66 µB/f.u. The observed Hc value is much lower than expected for a simple antiferromagnet consisting of magnetic moments of the order of 1 µB with TN > 40 K. No MT shows up in the a-axis field up to 14 T. At low temperatures, MT is a first order magnetic phase transition (FOMPT) and shows an asymmetric hysteresis. Hc decreases with increasing temperature while the hysteresis shrinks with increasing temperature and eventually vanishes at 28 K. The character of MT dramatically changes at this temperature from FOMPT to a second order magnetic phase transition (SOMPT) which is observed for 28 K < T < TN) as manifested by the change of character of magnetization and specific-heat anomalies. To understand the observed phenomena further we have performed first-principles electronic structure calculations focused on magnetism in UIrSi3. The corresponding results of experiments and calculations as concerns the type of anisotropy and the magnitude of anisotropy energy show reasonable agreement whereas the agreement on the size of the U magnetic moment depends on the calculation method. Both the experiment and theory suggest that the magnetically compensated ground-state of the system is not a simple two-sublattice antiferromagnet of up-down- up-down type but has a more complex nature. Experimental and Computational details The process of preparation of a UIrSi3 single crystal was started by synthesis of a stoichiometric polycrystal from pure elements and casting a rod ( 6.5 mm, length 85 mm). High purity elements: U (99.9%), Ir (99.99%) and Si (99.999%) were used. The obtained ingot was mounted in a four-mirror optical furnace (by Crystal Systems Corporation) optimized for the floating zone melting method. The middle part of the final product was annealed at 700°C for 10 days. Energy dispersive x-ray analysis confirmed the presence of the single UIrSi3 phase in the annealed product. The lattice parameters a = 417.22 pm and c = 996.04 pm of the tetragonal BaNiSn3-type structure determined by the x-ray powder 3 diffraction on a pulverized piece of the single crystal are in reasonable agreement with the literature 21. The U ions are coordinated solely within uranium basal plane layers. Each U ion has four U nearest neighbors located within the same basal plane and separated by dU-U = 417.22 pm ( = a). The magnetization and specific-heat measurements were carried out with a PPMS apparatus (Quantum Design Inc.) in magnetic fields applied along the c-axis up to 14 T. For determination of TN from the temperature dependence of specific heat, the point of the balance of the entropy released at the phase transition was taken. The field dependence of the specific heat was measured point by point in a stable magnetic field. At each point the measurement was repeated four times. The magnetic moments, easy magnetization axis, magnetocrystalline anisotropy energy, equilibrium volume and stability of antiferromagnetic structures were calculated using the methods based on density functional theory (DFT). We used the computer codes full potential local orbitals (FPLO)23, full potential augmented plane waves plus local orbitals (APW+lo)24 and in-house augmented spherical waves (ASW)25 to solve single particle Kohn-Sham equations. We treated the 5f states as itinerant Bloch states in all three methods and since no information about ground state magnetic structure is available the simple ferromagnetic and antiferromagnetic arrangements of moments were applied. The fully relativistic Dirac four- component mode was used in all FPLO calculations. For calculations with FPLO code we used the division 24×24×24 for both the a- and c-axes corresponding to 1764 and 3756 irreducible k-points in the Brillouin zone, respectively, to ensure the convergence of results. Since the total magnetic moment obtained from relativistic calculations was too small in comparison with the experimental one the orbital polarization correction26 was applied in the FPLO code.